On 20 Okt., 09:53, Graham Cooper <grahamcoop...@gmail.com> wrote: > On Oct 20, 4:53 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 19 Okt., 23:17, Uergil <Uer...@uer.net> wrote: > > > > If I recall WM's definitions correctly, the T1 sequence of triangles has > > > a fixed top vertex but the T2 sequence does not but does have a more or > > > less fixed center, so that their expansions are in different directions, > > > and no points have the same positions in both. > > > It is not necessary to have a coordinate system. You only need a > > sequence like this. > > > 1 > > > 1 > > 23 > > > 1 > > 23 > > 456 > > > .. > > > Are there three limits of the cardinal numbers of the sets that form > > the sides? > > > And if yes, why are the different in matheology? > > > Regards, WM > > OK I'll point out 1 difference. > > If you consider the rows > > 1 is fixed width > 23 is fixed width > .. > > If you consider the columns > > 1 > 2 > 4 > > is incomplete > > 3 > 5 > > is incomplete > > Herc
My point is, that every finite side is complete. Therefore a difference in the limit cannot occur. If it does nevertheless, then this shows simply that there is no limit, neither for columns nor for lines. There is no finished infinite number of finite numbers.
"Incomplete" is not a limit but only the possibility to add a further line with n numbers at position n.
It is simply nonsense to calculate a limit of a divergent sequence. That is shown in my little example to hold also for limit ordinals.